The British Palladium: Or, Annual Miscellany of Literature and Science for the Year ..., Volumen7D. Steel., 1757 |
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Página 1 - Containing many ufeful and entertaining Particulars, peculiarly adapted to the ingenious Gentlemen engaged in the delightful Study and Practice of the MATHEMATICKS.
Página 33 - Therefore, all the four fides of the trapezium DCEB being given, the area will be a maximum when the figure is infcribed in a circle. But the...
Página 47 - ... ceafe to touch the faid vertical plane ? how long will it then have been in motion? and how far from the point A will the end (m) ftrike the horizontal plane ? PRIZE QUESTION, ly M>r.
Página 31 - ... given point D, draw BDP -, to which, from A, apply AP equal to the bafe AC ; draw DF, FG, GH parallel to AP, AC and FD refpeftively ; and the thing is done.
Página 46 - ... and the explofion of the piece at the fame inftant of time, allowing the velocity of the ball to be to that of found in proportion of 3 to 2 r Attfwered ¿y Air.
Página 33 - GH = CD; in BH (when drawn) take BD of the given length; and from D, to BA and BC, apply DA and DC alfo of the given lengths; from whence the points A and C, and confequently the A ABC itfelf, will be determined.
Página 32 - AB, &c. and confequently, that F will be the center of gravity of the given triangle ABC. Hence the three required perpendiculars are found to be j'i9i5, 4*4095, and ^'6143, and their continual produft = I54'33- WWR The fume anfwered ty Mr.
Página 46 - What number of fhecp did he buy? VII. QUESTION 427, by Mr. T. Mofs. The rectangle under the two diagonals of any trapezium drawn into twice the cofine of the angle contained by them' (the radius being i) is equal to the difference of the aggregates of...
Página 41 - ... by the pendulum on the top of the mountain will then be only the half of (— '-) what it is above found to be: Therefore the height of the mountain will come out four times as great here, as when the mountain's attraction is neglected.* XIV. QUESTION 419 anfiutr:d Ij Mr.
Página 32 - FGxFHxFIisa maximum, the product thereof by the conftant quantity 4-ABx4-BCx4-AC, will alfo be a maximum •, that is, the product of the three parts ABF, BCF, and ACF of the given triangle, will be a maximum, and confequentljr thofe parts equal among themfelves ; fince it is evident (from Eu.